We prove an ultrametric q-difference version of the Maillet-Malgrange theorem on the Gevrey nature of formal solutions of nonlinear analytic q-difference equations. Since deg q and ord q define two valuations on C(q), we obtain, in particular, a result on the growth of the degree in q and the order at q of formal solutions of nonlinear q-difference equations, when q is a parameter. We illustrate the main theorem by considering two examples: a q-deformation of Painleve II, for the nonlinear situation, and a q-difference equation satisfied by the colored Jones polynomials of the figure 8 knots, in the linear case. We also consider a q-analog of the Maillet-Malgrange theorem, both in the complex and in the ultrametric setting, under the assumption that |q| = 1 and a classical diophantine condition.